Simplify Square Root of 62557

Here we will show you two methods that you can use to simplify the square root of 62557. In other words, we will show you how to find the square root of 62557 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√62557 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 62557 to simplify the square root of 62557. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 62557. The factors of 62557 are 1, 11, 47, 121, 517, 1331, 5687, and 62557. Furthermore, the greatest perfect square on this list is 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Calculate 62557 divided by the greatest perfect square from the list of all factors of 62557. We determined above that the greatest perfect square from the list of all factors of 62557 is 121. Furthermore, 62557 divided by 121 is 517, therefore B equals 517.

Now we have A and B and can get our answer to 62557 in its simplest radical form as follows:

√62557 = A√B

√62557 = 11√517

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 62557 to simplify the square root of 62557 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 62557 and then take the square root of that product. The prime factors that multiply together to make 62557 are 11 x 11 x 11 x 47. When we strip out the pairs only, we get 11 x 11 = 121 and the square root of 121 is 11. Therefore, A equals 11.

B = Divide 62557 by the number (A) squared. 11 squared is 121 and 62557 divided by 121 is 517. Therefore, B equals 517.

Once again we have A and B and can get our answer to 62557 in its simplest radical form as follows:

√62557 = A√B

√62557 = 11√517

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Simplify Square Root of 62558
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